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Hereditary Genius
27
who intermarried freely, and who had lived for many generations under
constant conditions; then the average height of the male adults of that
population would undoubtedly be the same year after year. Also—still
arguing from the experience of modern statistics, which are found to give
constant results in far less carefully-guarded examples—we should
undoubtedly find, year after year, the same proportion maintained between
the number of men of different heights. I mean, if the average stature was
found to be sixty-six inches, and if it was also found in any one year that
100 per million exceeded seventy-eight inches, the same proportion of 100
per million would be closely maintained in all other years. An equal
constancy of proportion would be maintained between any other limits of
height we pleased to specify, as between seventy-one and seventy-two
inches; between seventy-two and seventy-three inches; and so on.
Statistical experiences are so invariably confirmatory of what I have stated
would probably be the case, as to make it unnecessary to describe
analogous instances. Now, at this point, the law of deviation from an
average steps in. It shows that the number per million whose heights range
between seventy-one and seventy-two inches (or between any other limits
we please to name) can be predicted from the previous datum of the
average, and of any one other fact, such as that of 100 per million
exceeding seventy-eight inches.
The diagram on p. 28 will make this more intelligible. Suppose a million of
the men to stand in turns, with their backs against a vertical board of
sufficient height, and their heights to be dotted off upon it. The board would
then present the appearance shown in the diagram. The line of average
height is that which divides the dots into two equal parts, and stands, in the
case we have assumed, at the height of sixty-six inches. The dots will be
found to be ranged so symmetrically on either side of the line of
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